A two-layer approach to modelling the transformation of dilute pyroclastic currents into dense pyroclastic flows

2010 ◽  
Vol 467 (2129) ◽  
pp. 1348-1371 ◽  
Author(s):  
Emma E. Doyle ◽  
Andrew J. Hogg ◽  
Heidy M. Mader
Keyword(s):  
Single Layer ◽  
Pyroclastic Flows ◽  
Constant Density ◽  
Particle Collisions ◽  
Layer Model ◽  
Fluid Turbulence ◽  
Naturally Occurring ◽  
Dense Granular Flow ◽  
Two Layer Model ◽  
End Members

Most models of volcanic ash flows assume that the flow is either dilute or dense, with dynamics dominated by fluid turbulence or particle collisions, respectively. However, most naturally occurring flows feature both of these end members. To this end, a two-layer model for the formation of dense pyroclastic basal flows from dilute, collapsing volcanic eruption columns is presented. Depth-averaged, constant temperature, continuum conservation equations to describe the collapsing dilute current are derived. A dense basal flow is then considered to form at the base of this current owing to sedimentation of particles and is modelled as a granular avalanche of constant density. We present results which show that the two-layer model can predict much larger maximum runouts than would be expected from single-layer models, based on either dilute or dense conditions, as the dilute surge can outrun the dense granular flow, or vice versa, depending on conditions.

Two-layer Model for Electroabsorption and Built-in Potential Measurements on a-Si:H pin Solar Cells

1996 ◽  
Vol 420 ◽  
Author(s):  
Lin Jiang ◽  
E. A. Schiff
Keyword(s):  
Solar Cells ◽  
Amorphous Silicon ◽  
Second Harmonic ◽  
Semiconductor Devices ◽  
Single Layer ◽  
Experimental Results ◽  
Layer Model ◽  
Two Layer Model ◽  
Organic Devices

AbstractModulated Electroabsorption (EA) measurements have been widely used to estimate built-in potentials (Vbi) in semiconductor devices. The method is particularly simple in devices for which the built-in potential is dropped in a single layer of the device. However, experimental results in amorphous silicon and organic devices can involve at least 2 layers. In the present paper we consider the information which can be obtained about 2-layer semiconductor devices from electroabsorption measurements. In particular we describe a 2-layer EA model appropriate to a-Si:H based pin solar cells, for which both the p+ and i layers contribute to the EA signal. We present an analysis of capacitance and second harmonic measurements which yields the EA coefficient for the p+ layer of the device, and we present measurements on a-Si:H pin devices which appear consistent with this analysis. Wavelength dependent EA then yields the built-in potential across the 2-layer device.

Internal hydraulic jumps in two-layer systems

2015 ◽  
Vol 787 ◽  
pp. 1-15 ◽  
Author(s):  
Peter G. Baines
Keyword(s):  
Energy Loss ◽  
Single Layer ◽  
Boussinesq Approximation ◽  
Maximum Speed ◽  
Hydraulic Jumps ◽  
Zero Energy ◽  
Layer Model ◽  
Two Fluids ◽  
Conjugate State ◽  
Two Layer Model

This paper describes a new model of internal hydraulic jumps in two-layer systems that places no restrictions (such as the Boussinesq approximation) on the densities of the two fluids. The model is based on that of Borden and Meiburg (J. Fluid Mech., vol. 276, 2013, R1) for Boussinesq jumps, and has the appropriate behaviour in various limits (single-layer, small amplitude, Boussinesq, infinite depth). The energy flux loss in each layer across the jump is positive for all realistic jumps, reaching a maximum for the jump with maximum speed. Larger-amplitude jumps are possible, with decreasing energy loss, down to the ‘conjugate state’ of zero energy loss. However, it is argued that such states may be difficult to realise in practice, and if formed, will tend to the jump with maximum speed. The energy loss is mostly in the contracting layer unless the density there is small. The two-layer model is extended to incorporate mixing between the layers within the jump, with mixing based on the Richardson number.

Internal bores: an improved model via a detailed analysis of the energy budget

2012 ◽  
Vol 703 ◽  
pp. 279-314 ◽  
Author(s):  
Zachary Borden ◽  
Eckart Meiburg ◽  
George Constantinescu
Keyword(s):  
Propagation Velocity ◽  
Single Layer ◽  
Propagation Speed ◽  
Analytical Models ◽  
Geometrical Parameters ◽  
Net Energy ◽  
Layer Model ◽  
Viscous Effects ◽  
Two Layer Model ◽  
Internal Bores

AbstractInternal bores, or internal hydraulic jumps, arise in many atmospheric and oceanographic phenomena. The classic single-layer hydraulic jump model accurately predicts the bore height and propagation velocity when the difference between the densities of the expanding and contracting layers is large (i.e. water and air), but fails in the Boussinesq limit. A two-layer model, which conserves mass separately in each layer and momentum globally is more accurate in the Boussinesq limit, but it requires for closure an assumption about the loss of energy across a bore. It is widely believed that bounds on the bore speed can be found by restricting the energy loss entirely to one of the two layers, but under some circumstances, both bounds overpredict the propagation speed. A front velocity slower than both bounds implies that, somehow, the expanding layer is gaining energy. We directly examine the flux of energy within internal bores using two- and three-dimensional direct numerical simulations and find that although there is a global loss of energy across a bore, a transfer of energy from the contracting to the expanding layer causes a net energy gain in the expanding layer. The energy transfer is largely the result of turbulent mixing at the interface. Within the parameter regime investigated, the effect of mixing is much larger than non-hydrostatic and viscous effects, both of which are neglected in the two-layer analytical models. Based on our results, we propose an improved two-layer model that provides an accurate propagation velocity as a function of the geometrical parameters, the Reynolds number, and the Schmidt number.

Stokes Drift in Internal Equatorial Kelvin Waves: Continuous Stratification versus Two-Layer Models

2014 ◽  
Vol 44 (2) ◽  
pp. 591-599 ◽  
Author(s):  
Jan Erik H. Weber ◽  
Kai H. Christensen ◽  
Göran Broström
Keyword(s):  
Kelvin Waves ◽  
Stokes Drift ◽  
Constant Density ◽  
Inviscid Fluid ◽  
Layer Model ◽  
Constant Depth ◽  
Equatorial Undercurrent ◽  
The Pacific ◽  
Order Of Magnitude ◽  
Two Layer Model

Abstract The Stokes drift in long internal equatorial Kelvin waves is investigated theoretically for an inviscid fluid of constant depth. While the Stokes drift in irrotational waves is positive everywhere in the fluid, that is, directed along the phase velocity, this is not always the case for internal Kelvin waves, which possess vorticity. For constant Brunt–Väisälä frequency, the Stokes drift in such waves is sinusoidal in the vertical with a negative value in the middle of the layer for the first baroclinic mode. For a pycnocline that is typical of the equatorial Pacific, this study finds for the first mode that the largest negative Stokes drift velocity occurs near the depth where the Brunt–Väisälä frequency has its maximum. Here, estimated drift values are found to be on the same order of magnitude as those observed in the Pacific Equatorial Undercurrent at the same level. In contrast, a two-layer model with constant density in each layer yields a positive Stokes drift in both layers. This contradicts the fact that, as shown in this paper, the vertically integrated Stokes drift (the Stokes flux) must be zero for arbitrary Brunt–Väisälä frequency.

Coherent structures of nonlinear barotropic-baroclinic interaction in unequal depth two-layer model

2021 ◽  
Vol 408 ◽  
pp. 126347
Author(s):  
Jiaqi Zhang ◽  
Ruigang Zhang ◽  
Liangui Yang ◽  
Quansheng Liu ◽  
Liguo Chen
Keyword(s):  
Coherent Structures ◽  
Layer Model ◽  
Two Layer Model

A multi-layer model for nonlinear internal wave propagation in shallow water

2012 ◽  
Vol 695 ◽  
pp. 341-365 ◽  
Author(s):  
Philip L.-F. Liu ◽  
Xiaoming Wang
Keyword(s):  
Wave Propagation ◽  
Internal Wave ◽  
Shallow Water ◽  
Internal Waves ◽  
Bottom Topography ◽  
Laboratory Data ◽  
Constant Density ◽  
Layer Model ◽  
Fluid System ◽  
Nonlinear Internal Wave

AbstractIn this paper, a multi-layer model is developed for the purpose of studying nonlinear internal wave propagation in shallow water. The methodology employed in constructing the multi-layer model is similar to that used in deriving Boussinesq-type equations for surface gravity waves. It can also be viewed as an extension of the two-layer model developed by Choi & Camassa. The multi-layer model approximates the continuous density stratification by an $N$-layer fluid system in which a constant density is assumed in each layer. This allows the model to investigate higher-mode internal waves. Furthermore, the model is capable of simulating large-amplitude internal waves up to the breaking point. However, the model is limited by the assumption that the total water depth is shallow in comparison with the wavelength of interest. Furthermore, the vertical vorticity must vanish, while the horizontal vorticity components are weak. Numerical examples for strongly nonlinear waves are compared with laboratory data and other numerical studies in a two-layer fluid system. Good agreement is observed. The generation and propagation of mode-1 and mode-2 internal waves and their interactions with bottom topography are also investigated.

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